ZURICH, Jan 22 (Reuters) - Luxury goods maker Richemont on Monday offered up to 2.8 billion euros ($3.42 billion) to buy the shares in Yoox Net-A-Porter that it does not already own in a deal aimed at boosting the Swiss company's online presence.

The offer for 38 euros per share for the 75 percent of ordinary shares that Richemont does not own represents an almost 26 percent premium to Yoox Net-A-Porter's (YNAP) closing price on Friday.

In 2015, Yoox bought Richemont's Net-A-Porter unit in a transaction that gave the Swiss company 48.9 percent of YNAP but only voting rights of 25 percent and left the Italian company's management in charge.

Now seeking to take control, Richemont Chairman Johann Rupert said he sees a "meaningful opportunity" to strengthen YNAP's position in luxury e-commerce, including by expanding to new markets and adding to the product range.

"We are very pleased with the results achieved by Yoox Net-A-Porter Group's management team, led by Federico Marchetti, and we intend to support them going forward to execute their strategy and further accelerate the growth of the business," Rupert said in a statement.

Richemont, the owner of luxury brands Cartier, IWC and Dunhill, announced the deal after the Italian company waived provisions stemming from the 2015 transaction that would have prevented Richemont from boosting its stake.

YNAP's shares would be delisted from the Milan exchange, according to terms of the deal. ($1 = 0.8179 euros) (Reporting by John Miller; Editing by Muralikumar Anantharaman and Louise Heavens)